1929 L. DE BROGLIE or to a first approximation if the corrections introduced by the theory of relativity are negligible ith E=w- moc The constant energy w of the corpuscle is still as- sociated with the constant frequency y of the wave by the relation while the wavelength a which varies from one point to another of the force field is associated with the equally variable quantity of motion p by the fol- lowing relation x2)=p(xy2) lere again it is demonstrated that the group velocity of the waves is equal to the velocity of the corpuscle. The parallelism thus established between the orpuscle and its wave enables us to identify Fermat's principle for the waves and the principle of least action for the corpuscles(constant fields). Fermat's principle states that the ray in the optical sense which passes through two points A and B in a medium having an index n(xyz)varying from one point to another but constant in time is such that the integral aken along this ray is extreme. On the other hand Maupertuis principle least action teaches us the following: the trajectory of a corpuscle passi through two points A and B in space is such that the integral p taken along the trajectory is extreme, provided, of course, that only the motions corresponding to a given energy value are considered. From the relations derived above between the mechanical and the wave parameters, we have C I h hz一P const250 1929 L. DE BROGLIE or to a first approximation if the corrections introduced by the theory of relativity are negligible with E = W - m0c2. The constant energy W of the corpuscle is still as￾sociated with the constant frequency Y of the wave by the relation while the wavelength 1 which varies from one point to another of the force field is associated with the equally variable quantity of motion p by the fol￾lowing relation Here again it is demonstrated that the group velocity of the waves is equal to the velocity of the corpuscle. The parallelism thus established between the corpuscle and its wave enables us to identify Fermat’s principle for the waves and the principle of least action for the corpuscles (constant fields). Fermat’s principle states that the ray in the optical sense which passes through two points A and B in a medium having an index n(xyz) varying from one point to another but constant in time is such that the integral A I B nd2 taken along this ray is extreme. On the other hand Maupertuis’ principle of least action teaches us the following: the trajectory of a corpuscle passing through two points A and B in space is such that the integral I “pdl A taken along the trajectory is extreme, provided, of course, that only the motions corresponding to a given energy value are considered. From the relations derived above between the mechanical and the wave parameters, we have: